Tag Archives: theory

Today while teaching my Jazz Theory & Aural Skills class at DU, I had a revelation – a way of explaining the notion of “secondary dominant” chords by appealing to concepts and terminology from the TV show “Downton Abbey” (or substitute your favorite show, movie, or book about British aristocracy). Sound far-fetched? Read on.

As many musicians know, “most” chords in “most” songs are diatonic, meaning they consist exclusively of notes that are in the key. So in the key of C, we expect to see C, Dmi, Emi, F, G, Ami, and Bdim chords as triads, or Cma7, Dmi7, Emi7, Fma7, G7, Ami7, and Bmi7b5 as seventh chords, since these chords consist of notes from the key of C. We often label these chords with Roman numerals: I, ii, iii, IV, V, vi, and viiø. But most songs also include at least a few chords that are not diatonic – chords that include at least one note not in the key. The majortiy of these non-diatnoic chords fall into a few basic categories that explain the function of the chord, and by far the most important such category is the “secondary dominant”.

OK, I know, I promised you Downton Abbey, and so far, the hasn’t been an earl in sight. Well, here’s the deal. The most important relationship in music is V-I. That is, the most important chord in music is the I chord (called the “tonic”), and the V chord (called the “dominant”) serves to lead to the I chord. We could even say that the I chord is so important – wait for it – so important that it gets its own personal valet, the V chord. V for valet (pronounced, in Britain, to rhyme with “palette”), get it?

In the key of C, this is to say that G7 typically leads to Cma7. But sometimes, other chords like to feel important too. Sometimes, for instance, the ii chord – Dmi7 – wants to feel important. How do we make that happen? We give him his own personal valet too, of course! That is, we give him his own personal V chord. In the key of D minor, the V chord would be A7. We could say that A7 is the valet of Dmi7. Or, in Roman numeral terms, we could say it is the V of ii. In traditional classical notation, that is written V/ii, read as “V of ii”.

We’re still in the key of C, so Cma7 – the I chord – is still the earl of the estate. And G7 is still the primary valet – the personal valet of the I chord. But A7 chords do often occur as the personal valets of the ii chord, Dmi7. Chords like A7 – not the primary valet (the actual V chord in the key), but valets of some other diatonic chord – might be called secondary valets. The valets of ii, and of iii, and of IV, and of V, and of vi, are all common chords. So in the key of C, we may see A7 chords that lead to Dmi7 (V/ii leading to ii), B7 chords leading to Emi (V/iii leading to iii), C7 chords leading to Fma7 (V/IV leading to IV), D7 chords leading to G7 (V/V leading to V), or E7 chords leading to Ami7 (V/vi leading to vi).

These are the most common non-diatonic chords there are. And these chords that I am calling secondary valets in reference to Downton Abbey are, of course, actually called “secondary dominants”. Dominant = V, and V is for valet. So there you have it!

Some day, I’ll explain how a “suspension” can be explained using the Wile E. Coyote and The Road Runner cartoons.

The Gift of Jazz winter courses offered by professional pianist, composer, and educator Marc Sabatella begin on January 26, 2013.

The theme to this series of courses is Modal Jazz, a phrase that encompasses the music of Miles Davis’ “Kind of Blue”, John Coltrane’s “A Love Surpeme”, Herbie Hancock’s “Maiden Voyage”, Wayne Shorter’s “Speak No Evil”, and much more. The primary aspect of modal jazz that we will be looking at is the idea of using scales as the harmonic foundation of composition and improvisation.

Some of the most beloved jazz recordings of all time are based on relatively sparse composed material – most notably, Miles Davis’ “Kind of Blue” and John Coltrane’s “A Love Supreme”. These deceptively simple foundations allows the performers to build their own structures, improvising with just a few scales rather than being locked into a predictable chord progression. At the same time, composers like Herbie Hancock and Wayne Shorter extended the vocabulary of jazz harmony to include unique but more complex sonorities that also encourage the use of scales as improvisational tools. In this class, we will learn to create compositions that go beyond conventional harmonies and provide different types of frameworks for jazz performance. The final projects will be performed by a professional combo at Dazzle.

Improvisation in modal jazz involves learning a set of scales and developing the ability to create melodies with them. This is something most musicians have always done using the major scale, minor, and/or blues scales, but modal jazz introduces other possibilities. In this class, we will learn a number of other useful scales and when/how to use them, playing over tunes by people like Miles Davis, John Coltrane, and others. This course culminates in an (optional) performance at Dazzle.

Work on soloing and playing in a combo setting with a special emphasis on the modal jazz – music that encourages the use of a variety of scales as a basis for improvisation. This course culminates with a performance at Dazzle.

Space in all classes is extremely limited.Discounted tuition is available for students interested in taking more than one class.To enroll click here! (tuition is non-refundable unless the class is not held).

Here is a chapter-by-chapter summary of the book. There is enough detail here that if you are so inclined, you can actually learn quite a bit just from studying this. You will have to do a lot more work on your own to figure out all the applications, of course. But I hope the amount of information I provide here will be sufficient to convince you to buy the book!

Introduction

This purpose of this book is to help you improve your skills in playing standards, by which I mean the songs of George Gershwin, Cole Porter, and others. The harmony used in these songs is actually quite similar to the harmony found in classic music, and is variously referred to as tonal or functional harmony.

Previous generations of jazz musicians often learned hundreds or even thousands of standards by ear and are able to play them in any key, with improvised variations on the chord progressions. For various reasons, however, few younger jazz musicians learn as many of these songs or the skills involved in playing them by ear or transposing and reharmonizing them on the fly.

I believe that one key to these skills is the ability to understand chord progressions at a more intuitive level. We are able to play melodies by ear and transpose them because we can understand melodies in this way. We do not usually think in terms of “memorizing” a melody one note at a time. We hear and remember most melodies in phrases, not as a series of unrelated pitches. If the melody is random or atonal in nature, this does not apply, but it works for most standards. The same is true of lyrics. We do not normally learn lyrics one letter at a time, or even one word at a time, but as a series of phrases that have meaning. If the lyrics to a song are in a foreign language we do not understand, we have much greater difficulty learning them. And this is precisely the problem most of us experience with chord progressions – they are written in what is essentially a foreign language. Fortunately, as with any other language, it is possible to learn the language of harmony.

Scales And Chords

The starting point in the study of harmony is learning major and minor scales and the various chord types. I expect that most readers will already have a good working knowledge of this material, but I include this chapter for the benefit of those who need the review, and to establish a common set of definitions and concepts for subsequent chapters.

I start by demonstrating the major scale and how each scale defines a key. I also explain the concept of key signature, and introduce the circle of fifths.

The real core of the chapter comes as I list and define the various types of chords. I start with the triads found diatonically within a major scale, then move on to the different types of diatonic seventh chords. I then introduce the various extensions and alterations that can be made to those seventh chords, as well as seventh chords that are not found within the major scale. I also briefly describe some other chords types, including sixth chords, suspended chords, and polychords. Next I describe the natural or pure minor scale and the chords diatonic to it, saving a full exploration of the different minor scales until later.

The most important concept that I establish in this chapter is that while there are many different types of chords, in the study of tonal harmony they can all be classified according to one of six categories or qualities. These correspond to the basic types of seventh chords, and are as follows: major seventh chords, dominant seventh chords, minor seventh chords, tonic minor chords, half-diminished chords, and fully diminished chords. This section, entitled Chord Quality, is the one part of this chapter that everyone should read, including musicians already familiar with the basics of chord construction.

Functional Harmony

In the introduction, I state that rules in harmony are like the law of gravity – they do not tell you what you must do or not do, but instead simply describe cause and effect. For this reason, I prefer the term “guidelines” to “rules”. This chapter examines the guidelines employed in functional harmony, showing why certain combinations of chords tend to be used in certain ways.

The complete set of rules is a little longer than I had hoped, but several of them are just variations on or corollaries to others, or are pretty obvious but are included for the sake of completeness:

Any diatonic chord can be used at any time.

The dominant (V) tends to resolve to the tonic (I).

Any chord that contains a minor seventh interval between the root and seventh will tend to resolve downward by fifth.

Chords with a major seventh interval between the root and seventh are stable.

The IV chord can resolve satisfactorily to the I chord.

Any diatonic chord can resolve downward by perfect fourth to another diatonic chord.

Any diatonic chord can be replaced by another diatonic chord that has two tones in common with the original chord, when considered as triads.

The viiº chord may be played as a fully diminished seventh chord, particularly when it substitutes for V.

If one chord can substitute for another, then the original chord may be left in place and the substitute chord may be inserted either before or after it.

Any major, dominant, or minor chord may be preceded by a chord that tends to resolve to the original chord.

Any time we have a ii-V progression, we can simplify it to V.

Any major, dominant, or minor chord may be preceded by the dominant seventh chord a fifth above.

Any major, dominant, or minor chord can be preceded by a diminished chord a half step below.

Any two chords whose bass notes are a whole step apart may be connected by the diminished chord whose root is between the other two chords.

A major or minor chord may be preceded by a diminished chord built on the same root, without affecting the resolution of the preceding chord to the target chord.

The iv chord can substitute for the IV chord in a IV-I progression.

In a iv-I progression, the bVII7 chord may be inserted after or even replace the iv chord.

Any dominant seventh chord that resolves downward by fifth may be replaced by the dominant seventh chord a tritone away.

In a minor key, any chord diatonic to the harmonic or natural minor can be used at any time; the harmonic minor is usually preferred.

When tonicizing a minor chord with a secondary dominant or secondary ii-V, the use of a b5 on the ii chord and a b9 and b13 on the V chord reinforces the motion toward a minor key.

A minor key progression may use the i6, IV, or viØ chords from the melodic minor.

A minor key progression may borrow the I chord, or other chords, from the parallel major.

Common Idioms

While the guidelines listed in the previous chapter can explain most of what happens in tonal chord progressions, we can usually simplify our understanding of a song considerably. Just as there are many possible chord types but they all fall into one of six basic qualities, we can divide most harmonic phrases into one of a few basic categories. To a large extent, phrases within a category are interchangeable, so not only does learning a song reduce to just recognizing its structure in terms of these categories, but once we have done so, we also have the tools we need to reharmonize the song by substituting other idioms from within the same categories.

Just as we can usually break a song down into a handful of broad sections such as AABA, we can usually break down each section into a handful of these idiomatic phrases. The phrases I am talking about are usually around two measures each. At slower tempos they may be squeezed into a single measure, and at faster tempos they might take four measures each. The categories of phrases I have identified are described below.

Cadential Progressions

Cadential progressions are phrases like the familiar ii-V-I cadence whose purpose is to lead us back to the tonic or I chord. Also in this category are the iv-I and iv-bVII7-I minor plagal progressions covered in the previous excerpt. There are a number of other examples, and in this section, I present a few of them and show how the guidelines from the previous chapter can be used to derive these cadences. I also hope to get you to hear that despite the differences between them, they are all serving the same function – to lead us back to the tonic.

Precadential Progressions

If a cadence is something that leads us back to the tonic, a precadential progression is something that leads us to a cadence. In practice, this most often means something that leads to the ii chord, since that is the most common way to begin a cadence. There are quite a few different commonly occurring idioms that serve as precadential progressions, such as I-IV-iii-VI, I-VII-bVII-VI, and I-ii-iii-#iiº. Recognizing how these progressions all work to serve the same function is the purpose of this section.

Note that while most precadential progressions begin with the tonic, it is possible to begin a precadential progression from the ii, iii, IV, or vi chords as well. These progressions are discussed separately, as they are interchangeable if they start from the same place.

Static Progressions And Turnarounds

Sometimes, a song just needs to stay around the tonic for a while. This is especially common at the beginning of a tune, where I call them static phrases. It is also common at the end of an eight-bar section, where we typically reach the I chord at the beginning of bar seven and then need to fill space until we reach the I chord at the beginning of the next section. Static phrases that occur in this context are also called turnarounds.

While the simplest static progression is just to stay on I throughout, other variations may consist of a short precadential phrase paired with a short cadence, as in the ubiquitous I-VI-ii-V. Other possibilities occur as well, such as I-ii-iii-ii or I-I7-IV-#ivº. Again, the purpose of this section is to help you recognize how each of these progressions works to perform the same function.

Transitional Progressions

I define a transitional progression as a phrase that appears to be leading us away from the tonic and toward one of the other diatonic chords, but does not actually constitute a modulation to a new key. Another term I sometimes hear for this is tonicization. The distinction between this and a modulation is that in the latter, once we reach our destination, we stay there a while, and see other phrases that function in the new key, whereas in a transition, the target chord immediately turns around and functions with respect to the original key.

Most transitions consist of a ii-V relative to the target chord. I sometimes refer to this as a secondary ii-V. For example, a transition to the vi chord might consist of a secondary ii-V leading to that vi chord, or, in other words, viiØ-III-vi.

Unlike with the previous categories of idioms, there are not usually many different ways of achieving a given transition, although there are a couple of different ways to transition to IV and also to vi. It is also true than you can substitute a transition to one chord for a transition to a different chord, if the target chords can substitute for each other. In practice, this means a transition to the IV can often be replaced by a transition to ii or to vi and vice versa.

However, instead of focusing on the different ways of transitioning to a given chord, the primary purpose of this section help you learn to hear the difference between the transitions. There are only four common transitions: to ii, iii, IV, and vi. We almost never see transitions to V or viiØ. In minor keys, it is the chords diatonic to the natural minor that serve as targets of transitions.

Modulations

A modulation is like a transition that sticks. Once we reach our target – which, unlike in a transition, is not necessarily a diatonic chord – we stay there long enough to have another phrase or two in the new key. In fact, once we reach the new key, we tend to see exactly the same types of phrases we saw in the original key: static progressions, cadences, and so forth. Thus the modulation itself – the motion into the new key – is the final category of phrase we must learn. And because there are so many potential targets for a modulation, this is often the most difficult type of phrase to learn to hear. We can instantly tell a modulation is occurring, but identifying the new key can be more difficult. Fortunately, as with transitions, there is usually only one way a modulation is actually accomplished – via a secondary ii-V. So the purpose of this section is to help you hear the different modulations.

This section includes examples taken from actual standards to demonstrate all of the different possible targets of a modulation. I explain how you can use the circle of fifths to help you decide where a modulation is going – you can learn to tell the different between a modulation in the sharper direction versus the flatter direction, and also between a modulation that is closely related on the circle versus one that is more distant.

This chapter concludes with a complete harmonic analysis of a standard, They Can’t Take That Away From Me, by George Gershwin. I manage to reduce this whole tune down to just a handful of easily heard and understood idioms.

Learning And Playing Songs

The final chapter of the book is where I show you how to go about applying all the information presented in previous chapters. In fact, rather than trying to master the preceding material before starting this chapter, I recommend just reading through the preceding material and then turning here to see how to really learn to use it in practice.

The basic practice regimen I describe involves learning tunes – a lot of tunes. For each tune, you will start by playing it from a lead sheet, then move on to playing it from memory, and finally transposing it into a few different keys. I give hints on how to apply your developing understanding of harmony to make both the playing from memory and the transposing go more smoothly. I stress using your ear at all steps along the way to help you establish the connection between theory on paper and the actual sounds of the music.

The key to the approach is to recognize the idioms used in the chord progressions. Rather than hear a 32-bar standard as consisting of 32 unrelated chords, you learn to hear it as just perhaps six or seven idiomatic phrases that all fall into one of just a few easily recognized categories. The idea is to use the process of learning tunes as a way of getting familiar with these idioms, and this in turn will make learning tunes easier.

You should find your skills in memorization and transposition improvising noticeably in a relatively short period of time. I also show how to apply these same skills to playing a song by ear when you do not have a lead sheet for it.

I then discuss how to apply your understanding of chord progressions to substitution and reharmonization, using the standard My One And Only Love by Guy Wood and Robert Mellin as an example. Looking at just the “A” section, I first break it down into a series of eight harmonic phrases and then show how to go about performing substitutions using other idioms from the same categories as well as more direct application of the guidelines of harmony themselves.

I conclude by discussing ways that your understanding of harmony can be an aid to improvisation and to composition. Although this is not a book about improvisation per se, I know that application to improvisation is an area that will be of special interest to a number of players.